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We develop a multiscale spatial kernel convolution technique with higherorder functions to capture fine scale local features and lower order terms tocapture large scale features. To achieve parsimony, the coefficients in themultiscale kernel convolution model is assigned a new class of "Tree shrinkageprior" distributions. Tree shrinkage priors exert increasing shrinkage on thecoefficients as resolution grows so as to adapt to the necessary degree ofresolution at any sub-domain. Our proposed model has a number of significantfeatures over the existing multi-scale spatial models for big data. In contrastto the existing multiscale approaches, the proposed approach auto-tunes thedegree of resolution necessary to model a subregion in the domain, achievesscalability by suitable parallelization of local updating of parameters and isbuttressed by theoretical support. Excellent empirical performances areillustrated using several simulation experiments and a geostatistical analysisof the sea surface temperature data from the pacific ocean.

Large Multi-scale Spatial Kriging Using Tree Shrinkage Priors